Filters are a basic and important component of a variety of electrical systems. Among the broad categories of electrical systems that use filters are communication systems such as optical, electrical and wireless communication systems and sensor systems, such as medical diagnostic systems, fire detection systems, object tracking systems, wireless controllers, smart cameras, and smart phones. Other general time series data processing systems include financial predictors.
Filters are, broadly speaking, used to facilitate the extraction of information from captured signals or any input data stream. Conventional filters perform this task by suppressing noise, thereby increasing the Signal to Noise Ratio (SNR). Conventional filters are designed to pass certain frequencies and block other frequencies. Frequency bands that include desired information are passed and out of band noise energy is blocked. Originally, filters used linear analog circuits. Since the advent of digital electronics Digital Signal Processing (DSP) filters have come into widespread use. Conventional DSP filters are also designed to pass certain frequencies and reject other frequencies.
Q-filters are a new class of adaptive nonlinear digital filters that are used in place of one or more conventional DSP filters. Q-filters are described in co-pending patent application Ser. No. 10/854,836 by M. Mohamed et al. which is assigned to the assignee of the invention described herein. Q-filters operation and kernel parameter estimation are described in Magdi Mohamed et al., Application of Q-Measures Techniques to Adaptive Nonlinear Digital Filtering, 2006 IEEE INTERNATIONAL CONGRESS ON COMPUTATIONAL INTELLIGENCE, 2006 IEEE INTERNATIONAL CONFERENCE ON FUZZY SYSTEMS, in Vancouver, BC, Canada, Jul. 16-21, 2006. A Q-filter is defined as a Choquet integral of the input signal with respect to a Q-measure over a window of the input signal values. Q-measures are described in M. Mohamed, Q-Measures: An Efficient Extension of the Sugeno Lambda-Measure, IEEE TRANSACTIONS ON FUZZY SYSTEMS, Vol. 11, No. 3, June 2003.
Although the Q-filters described in the previous work are versatile and work well, they include threshold stages and are somewhat more complicated then traditional DSP filters. In the interest of reducing processing time and lowering battery consumption in battery operated devices that include Q-filters, it would be desirable to provide more efficient implementation of Q-filters.
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